🚀 go-pugleaf

In the "\"FRACTAL\" discussion list" <FRAC-L%GITVM1.BITNET@uga.cc.uga.edu>
"Cliff Pickover (914 945-3630)" <CLIFF%YKTVMV.BITNET@uga.cc.uga.edu> wrote:

|>  Every year or so I ask the same question about the M-set.
|> Have we generally seen all there is to be seen?

Robert P Munafo <mrob@WORLD.STD.COM> replied to the list:

>My answer is an emphatic "no".  Most people who do not believe
>me will be convinced by using a program that plots with the
>Distance-Estimator method, and setting it to view the area of
>the complex plane centered at

  -1.769 110 375 463 767 386 0  +  0.009 020 388 228 023 439 7i

>with an edge length (height and width) of 6.4e-17 .  Make sure
>the number of iterations is at least 10,000.

In article <1993Aug28.013942.18928@ast.saic.com>, 
  hilljr@jupiter.saic.com (Jay R. Hill) writes in the 1-D M-set 
  thread:

> Take a look with fractint at these little Mandelbroties,
> especially at the 'tree' above them (in the +i direction).
> I was surprised to find a pattern that we like to make with
> iterated function systems fractals.  The pattern is


                  _|    |          \_
                    \___|   |   ___/
                    /    \  |  /   \_
                  _/      \ | /    |
                   |       \|/
                            |
                            |
                            |
                            |

These were observed in the sequence approaching -1.75:

> period     center        approx size
>   5  -1.6254137251233038  0.0020294
>   8  -1.7110794700131522  0.0000864
>  11  -1.7320062728696561  0.0000109
>  14  -1.7397176014514633  0.0000026
>  17  -1.7433378329345028  0.0000009
>  20  -1.7453196244460596  0.00000038
>  23  -1.7465233432992069  0.00000020
>  26  -1.7473107209745575  0.00000012
>  29  -1.7478549581283644  0.00000007
>  32  -1.7482474524728249  0.00000005

Now I ask, without displaying Robert's picture, has this
tree like pattern continued into the -1.75 cusp?  Maybe I
can make a GIF of this tonight.  Since there are several ways
to generate the tree pattern, such as iterated stick plots
and IFSs, it would be interesting to find their parameters
and compare the pictures with the MSet counterpart.

Warmly,
Jay "Not tonight honey, I'm viewing Robert's zoom" Hill
-- 
{ hilljr@jupiter.saic.com } begin writeln(3*ln(640320)/sqrt(163):17:15) end.
void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;
for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);
printf("%17.15lf\n",1/a);}